Adaptive fuzzy PIMD controller for systems with uncertain deadzones

In this paper, a new adaptive fuzzy Proportional-Integral (of a modified error function)-Derivative (PIMD) controller is designed for systems with uncertain deadzones. Instead of using the summation of the system output error to be one of the input variables, the fuzzy mechanism in PIMD controller takes the summation of a proposed error function as one essential part of the output fuzzy singleton. Together, with the linearly combined error and difference of the error as the only input variables, the complexity reduced fuzzy mechanism of the fuzzy PIMD controller is constructed. The adaptation processes are provided to determine the parameters of the PIMD controller to reduce the overshoot and to accelerate the system with deadzone to the desired output. The fuzzy PIMD controller is indicated to be flexible to the variations of deadzone parameters. Also, the proposed fuzzy PIMD controller is flexible to the change of deadzone model to contain jump discontinuity points. Moreover, the fuzzy PIMD controller can perform well for the system with time-varying deadzone model. Simulation results are included to indicate the effectiveness of the adaptive fuzzy PIMD controller.     

Non-fragile multivariable PID controller design via system augmentation

In this paper, the issue of designing non-fragile H_∞ multivariable proportional-integral-derivative (PID) controllers with derivative filters is investigated. In order to obtain the controller gains, the original system is associated with an extended system such that the PID controller design can be formulated as a static output-feedback control problem. By taking the system augmentation approach, the conditions with slack matrices for solving the non-fragile H_∞ multivariable PID controller gains are established. Based on the results, linear matrix inequality -based iterative algorithms are provided to compute the controller gains. Simulations are conducted to verify the effectiveness of the proposed approaches.     

Robustness of fuzzy PID controller due to its inherent saturation

In this paper, an inherent saturation of the fuzzy proportional–integral–derivative (PID) controller is revealed due to the finite fuzzy rules used. An equivalent structure and model of the fuzzy rule base is derived to show a saturation property. The bandwidth of the fuzzy PID control system can be adjusted by changing saturation parameter. Parameters of the fuzzy PID controller can be designed based on the inherent saturation. Compared with the conventional PID controller, the fuzzy PID controller has two advantages because of the inherent saturation: (1) without the additional filter, it can prevent impulse signal effectively; (2) without the additional anti-windup structure, a robust performance can be maintained when the input saturation occurs. The fuzzy PID controller is applied to an integrated circuit curing process. The simulation and experiment results demonstrate these effects of the inherent saturation, and its influence to the robustness of fuzzy PID controller.     

基于小脑模型关节控制器与PID复合的高速公路交通流密度控制

高速公路交通控制系统是一个复杂的非线性时变系统, 传统的匝道控制方法难以取得满意的控制效果. 为此, 本文提出基于小脑模型关节控制器(CMAC)与PID复合的匝道控制方法. 首先建立了二阶宏观动态交通流模型, 然后研究了CMAC与PID复合控制算法, 结合非线性反馈理论, 设计了基于CMAC与PID复合的高速公路交通流密度控制器, 该密度控制问题是一个输出跟踪和扰动抑制问题, 最后采用两个仿真实例对该方法的有效性进行验证. 结果表明, 复合控制具有优越的密度跟踪性能和抑制噪声干扰的能力; 复合控制方法能够有效地消除交通拥挤, 并使主线车流趋于稳定.     

Robust self-tuning PID controller for nonlinear systems

In this paper, we propose a robust self-tuning PID controller suitable for nonlinear systems. The control system employs a preload relay (P_Relay) in series with a PID controller. The P_Relay ensures a high gain to yield a robust performance. However, it also incurs a chattering phenomenon. In this paper, instead of viewing the chattering as an undesirable yet inevitable feature, we use it as a naturally occurring signal for tuning and re-tuning the PID controller as the operating regime digresses. No other explicit input signal is required. Once the PID controller is tuned for a particular operating point, the relay may be disabled and chattering ceases correspondingly. However, it is invoked when there is a change in setpoint to another operating regime. In this way, the approach is also applicable to time-varying systems as the PID tuning can be continuous, based on the latest set of chattering characteristics. Analysis is provided on the stability properties of the control scheme. Simulation results for the level control of fluid in a spherical tank using the scheme are also presented.     

An optimal stochastic multivariable PID controller: a direct output tracking approach

This paper deals with the design of an optimal stochastic controller possessing tracking capability of any reference output trajectory in the presence of measurement noise. We consider multi-input multi-output linear time-invariant systems and a proportional-integral-derivative (PID) controller. The system under consideration needs not be stable. A recursive algorithm providing optimal time-varying PID gains is proposed for the case where the number of inputs is larger than or equal to the number of outputs. The development of the proposed algorithm aims for per-time-sample minimisation of the mean-square output error in the presence of erroneous initial conditions, measurement noise, and process noise. Necessary and sufficient conditions are provided for the convergence of the output error covariance. In addition, convergence results are presented for discretised continuous-time plants. Simulation results are included to illustrate the performance capabilities of the proposed algorithm. Performance comparison with an optimal stochastic iterative learning control scheme, an optimal PID controller, an adaptive PID controller, and a recent optimal stochastic PID controller are also included.     

Parallel Fuzzy P＋Fuzzy I＋Fuzzy D Controller： Design and Performance Evaluation

In this paper, a parallel fuzzy proportional plus fuzzy integral plus fuzzy derivative (FP+FI+FD) controller is proposed. It is derived from the conventional parallel proportional-integral-derivative (PID) controller. It preserves the linear structure of a conventional parallel PID controller, with analytical formulas. The final shape of the controller is a discrete-time fuzzy version of a conventional parallel PID controller. Computer simulations are performed to evaluate the performance of the FP+FI+FD controller for setpoint tracking and load-disturbance rejection for some complex processes, such as first- and second-order processes with delay, inverse response process with and without delay and higher order processes. Also, the performance of the proposed fuzzy controller is evaluated experimentally on highly nonlinear liquid-flow process with a hysteresis characteristic due to a pneumatic control valve. The simulation and real time control is done using National Instrument hardware and software (LabVIEW). The response of the FP+FI+FD controller is compared with the conventional parallel PID controller, tuned with the Ziegler-Nichols (Z-H) and Astrom-Hagglund (A-H) tuning technique. It is observed that the FP+FI+FD controller performed much better than the conventional PI/PID controller. Simulation and experimental results demonstrate the effectiveness of the proposed parallel FP+FI+FD controller.     

Evolving an interval type-2 fuzzy PID controller for the redundant robotic manipulator

Robotic manipulators are a multi-input multi-output, dynamically coupled, highly time-varying, complex and highly nonlinear systems wherein the external disturbances, parameter variations, and random noise adversely affects the performance of the robotic system. Therefore, in order to deal with such complexities, however, an intriguing task for control researchers, these systems require an efficient and robust controller. In this paper, a novel application of genetic algorithms (GA) optimization approach to optimize the scaling factors of interval type-2 fuzzy proportional derivative plus integral (IT2FPD+I) controllers is proposed for 5-DOF redundant robot manipulator for trajectory tracking task. All five controllers' parameters are optimized simultaneously. Further, a procedure for selecting appropriate initial search space is also demonstrated. In order to make a fair comparison between different controllers, the tuning of each of the controllers' parameters is done with GA. This optimization technique uses the time domain optimal tuning while minimizing the fitness function as the sum of integral of multiplication of time with square error (ITSE) for each joint. To ascertain the effectiveness of IT2FPID controller, it is compared against type-1 fuzzy PID (T1FPID) and conventional PID controllers. Furthermore, robustness testing of developed IT2FPID controller for external disturbances, parameter variations, and random noise rejection is also investigated. Finally, the experimental study leads us to claim that our proposed controller can not only assure best trajectory tracking in joint and Cartesian space, but also improves the robustness of the systems for external disturbances, parameter variations, and random noise.     

Design of a fractional order PID controller for an AVR using particle swarm optimization

Application of fractional order PID (FOPID) controller to an automatic voltage regulator (AVR) is presented and studied in this paper. An FOPID is a PID whose derivative and integral orders are fractional numbers rather than integers. Design stage of such a controller consists of determining five parameters. This paper employs particle swarm optimization (PSO) algorithm to carry out the aforementioned design procedure. PSO is an advanced search procedure that has proved to have very high efficiency. A novel cost function is defined to facilitate the control strategy over both the time-domain and the frequency-domain specifications. Comparisons are made with a PID controller and it is shown that the proposed FOPID controller can highly improve the system robustness with respect to model uncertainties.     

Decomposition of a fuzzy controller based on the inference break-up method

A concept called the decomposition of multivariable control rules is presented. Fuzzy control is the application of the compositional rule of inference and it is shown how the inference of the rule base with complex rules can be reduced to the inference of a number of rule bases with simple rules. A fuzzy logic based controller is applied to a simple magnetic suspension system. The controller has proportional, integral and derivative separate parts which are tuned independently. This means that all parts have their own rule bases. By testing it was found that the fuzzy PID controller gives better performance over a typical operational range then a traditional linear PID controller. The magnetic suspension system and the contact-less optical position measurement system have been developed and applied for the comparative analysis of the real-time conventional PID control and the fuzzy control.     

Teaching–learning based optimization algorithm based fuzzy-PID controller for automatic generation control of multi-area power system

This paper deals with the design of a novel fuzzy proportional–integral–derivative (PID) controller for automatic generation control (AGC) of a two unequal area interconnected thermal system. For the first time teaching–learning based optimization (TLBO) algorithm is applied in this area to obtain the parameters of the proposed fuzzy-PID controller. The design problem is formulated as an optimization problem and TLBO is employed to optimize the parameters of the fuzzy-PID controller. The superiority of proposed approach is demonstrated by comparing the results with some of the recently published approaches such as Lozi map based chaotic optimization algorithm (LCOA), genetic algorithm (GA), pattern search (PS) and simulated algorithm (SA) based PID controller for the same system under study employing the same objective function. It is observed that TLBO optimized fuzzy-PID controller gives better dynamic performance in terms of settling time, overshoot and undershoot in frequency and tie-line power deviation as compared to LCOA, GA, PS and SA based PID controllers. Further, robustness of the system is studied by varying all the system parameters from −50% to +50% in step of 25%. Analysis also reveals that TLBO optimized fuzzy-PID controller gains are quite robust and need not be reset for wide variation in system parameters.     

Harmony search algorithm-based fuzzy-PID controller for electronic throttle valve

The electronic throttle control (ETC) for a gasoline engine is a typical nonlinear plant because of its nonlinear spring and model-parameter changes caused by external environmental variables. In this paper, a fuzzy proportional-integral-derivative (PID) control strategy is proposed in order to improve the responsiveness of ETC. In the fuzzy-PID scheme, the input variables are the error signal and its derivative, and the output variable is PID gains expressed in terms of fuzzy rules. In this manner, the fuzzy-PID controller has more flexibility and capability than conventional ones. A novel technique to tune the fuzzy rules of fuzzy-PID controller is proposed using a harmony search algorithm, which can search the optimal PID gains for the plant. Simulation and experiment results have shown the effective performance of the proposed controller.     

船舶航向非线性系统的多滑模自适应模糊控制

针对参数未知的船舶航向非线性控制系统数学模型,在考虑舵机伺服机构特性的情况下,船舶航向控制问题就成为一个虚拟控制系数未知的非匹配不确定非线性控制问题.基于多滑模设计方法和模糊逻辑系统的逼近能力,提出了一种多滑模自适应模糊控制算法,通过引入非连续投影算法和积分型Lyapunov函数,提高了系统在抑制参数漂移、控制器奇异等方面的能力.借助Lyapunov函数证明了所设计控制器使最终的闭环非匹配不确定船舶运动非线性系统中的所有信号有界,且跟踪误差收敛到零.仿真研究表明:该算法与传统的PID控制相比,具有较好的跟踪能力和自适应能力.     

单神经元自适应PID控制器的性能优化设计

研究了单神经元自适应PID摔制器性能优化问题,阐述了该摔制器的特点、控制律;给出了一种控制灵敏度的快速近似求取方法,实现了PID参数的在线自学习;使单神经元控制器具有可调参数少、易于整定、控制输出平稳、鲁棒件强的独特优点,适用于大滞后且要求平稳控制输出的工业过程。     

基于粒子群算法的无线充PID控制器优化设计

对于谐振式无线充电系统,由于负载和线圈耦合变化等扰动影响,供电池负载充电的电流若只进行开环控制易产生扰动,故在前向通道中加入经典PID控制器,对系统进行实时有效的闭环控制。针对经典PID控制器的参数无法自适应整定的问题,提出了利用粒子群算法（PSO）自整定设计无线充电PID控制器参数的方法,并进行仿真分析和实验验证,结果表明：引入粒子群算法后的PID控制器快速性和稳定性都优于经典PID控制器,调节时间减少0.647s,最大超调量下降了4,1%,稳态误差误差下降了1.04%,证明了该方法对于改善无线充电系统输出动静态特性的可行性和有效性。     

自适应模糊PID控制器在跟踪器瞄准线稳定系统中的应用

针对陀螺惯性平台上的跟踪器瞄准线稳定系统中非线性不确定因素对稳定精度的影响, 设计了一种自适应模糊PID复合控制策略. 提出了改进的自适应调整因子和学习算法进行控制参数和规则的在线修正; 采用PID控制克服模糊控制固有的精度盲区. 实验结果表明该方法在一定测量噪声和速度敏感范围内, 能有效地隔离载体扰动,保证跟踪器对目标的准确瞄准, 具有动态响应快、稳定精度高、自适应抗干扰鲁棒性强等特点.     

Some investigations on fuzzy P + fuzzy I + fuzzy D controller for non-stationary process

The paper addresses the adaptive behaviour of parallel fuzzy proportional plus fuzzy integral plus fuzzy derivative (FP+FI+FD) controller. The parallel FP+FI+FD controller is actually a non-linear adaptive controller whose gain changes continuously with output of the process under control. Two non-stationary processes, whose characteristics change with time, are considered for simulation study. Simulation is performed using software LabVIEW TM . The set-point tracking response of parallel FP+FI+FD is compared with conventional parallel proportional plus integral plus derivative (PID) controller, tuned with the Ziegler-Nichols (Z-N) tuning technique. Simulation results show that conventional PID controller fails to track the set-point and becomes unstable as the process changes its characteristic with time. But the parallel FP+FI+FD controller shows considerably much better set-point tracking response and does not deviate from steady state. Also, a huge spike is observed in the output of PID controller as the reference set-point and process parameters are changed, while the FP+FI+FD controller gives spike free control signal.     

Single-loop controller design via IMC principles

In this paper, a new internal model control (IMC)-based single-loop controller design is proposed. The model reduction technique is employed to find the best single-loop controller approximation to the IMC controller. Compared with the existing IMC-based methods, the proposed design is applicable to a wider range of processes, and yields a control system closer to the IMC counterpart. It can be made automatic for on-line tuning. The users have the option to choose between PID and high-order controllers to suit the applications better. It turns out that high-order controllers may be necessary to achieve high performance for essentially high-order processes.     

一种基于遗传算法的非线性PID控制器

基于PID控制器各增益参数与偏差信号之间呈现非线性关系,拟合各参数的非线性函数可分别对控制器的P／I／D各部分实施单独调节的思想,提出根据控制与误差之间的调节规律,给定一组增益参数的非线性函数,并采用遗传算法来优化和构造此非线性PID调节器．典型系统的仿真结果表明,该控制器可在一定程度上兼顾系统的动态和静态性能．     

Advanced controller auto-tuning and its application in HVAC systems

In this paper, an advanced PID auto-tuner for both single- and multi-variable processes is described and its application to HVAC systems is presented. The auto-tuner exploits two different process identification methods to suit a wide range of processes. It incorporates two recent PID design rules to achieve high control performances for processes with different dynamic characteristics. Decoupling control is used for multivariable processes. The auto-tuner was implemented on a distributed control system and applied in industry. Experimental results demonstrate the effectiveness and superior performance of the implemented auto-tuner over the manually tuned PID controller and the standard relay auto-tuner.